Analysis and Evaluation of a Practical Downlink Multiuser MIMO Scheduler over LTE Advanced Massive MIMO Systems

ABSTRACT

Methods and a system are provided for enhanced long-term evolution scheduling. A ranking is constructed for one or more users scheduled on one or more resource blocks. A layer mapping is generated, using a finite modulation and coding scheme, utilizing the ranking of each of the one or more users for the one or more resource blocks. An enhanced ranking is determined, using a finite constraint on a buffer for each of the one or more users, for the one or more resource blocks utilizing the layer mapping. The enhanced ranking is deployed into a schedule for the one or more resource blocks being utilized by each of the one or more users. Bandwidth usage is optimized in the one or more resource blocks by utilizing the schedule.

RELATED APPLICATION INFORMATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 62/329,411 filed on Apr. 29, 2016, incorporated herein byreference in its entirety.

BACKGROUND Technical Field

The present invention generally relates to long-term evolution (LTE)systems and more particularly to a practical downlink (DL) multiusermulti-input-multi-output (MU-MIMO) scheduler over LTE advanced massiveMIMO systems.

Description of the Related Art

The MU-MIMO narrowband user selection problem has been analyzed mainlyfor the case when each user has one receive antenna and can be assignedone stream. In general, there is a coupling constraint in that a userthat is selected on multiple resource blocks (RBs) must be assigned thesame transmit rank on all those RBs, a.k.a. per-user rank constraint.The DL wideband MU-MIMO scheduling problem with the aforementionedper-user rank-constraint has been only considered for specific values ofthe input parameters (such as the maximum number of co-scheduled users,maximum rank per user etc.). Moreover, none of the prior algorithmsincorporate the decorrelation property of massive MIMO systems.

The theoretical limits for a broadcast channel under ideal conditionsand established the huge promise of MU-MIMO. This spurred investigationsthat have been ongoing for the past decade. Most of these investigationshave focused their attention on more practical yet asymptoticallyoptimal linear transmit precoding and have also considered the impact ofimperfect channel state information (CSI). The effort to standardize DLMU-MIMO has led to the adoption of precoded pilots in LTE-A. Theseprecoded pilots enable a scheduled user to directly estimate theeffective channel (which is the product of the DL channel matrix and thetransmit precoder). Thus, the base station (BS) is freed from the burdenof explicitly conveying the chosen precoder to the scheduled users andhence can fully optimize its choice of the precoding matrix. However,the performance results of MU-MIMO in frequency-division duplexing (FDD)systems equipped with a modest number of transmit antennas (typically 2or 4) have not lived up to the expectations. This is because obtainingCSI feedback that is accurate enough for MU-MIMO has proved to bechallenging given the feedback constraints placed in LTE. Moreover, thesmall number of transmit antennas that comprise of cross-polarizedantenna element pairs are useful for single-user (SU) MIMO but are notconducive to creating beams that enable good separation of differentusers in the signal space.

SUMMARY

According to an aspect of the present principles, a computer-implementedmethod is provided for enhanced scheduling on a long-term evolutionnetwork. The method includes constructing, by a processor, a ranking forone or more users scheduled on one or more resource blocks. The methodalso includes generating, by the processor using a finite modulation andcoding scheme, a layer mapping utilizing the ranking of each of the oneor more users for the one or more resource blocks. The methodadditionally includes determining, by the processor using a finiteconstraint on a buffer for each of the one or more users, an enhancedranking for the one or more resource blocks utilizing the layer mapping.The method further includes deploying, by the processor, the enhancedranking into a schedule for the one or more resource blocks beingutilized by each of the one or more users. The method also includesoptimizing, by the processor, bandwidth usage in the one or moreresource blocks by utilizing the schedule.

According to another aspect of the present principles, acomputer-implemented method is provided for enhanced scheduling on along-term evolution network. The method includes constructing, by aprocessor, a ranking for one or more users scheduled for an initialtransmission on one or more resource blocks. The method also includesgenerating, by a processor, an enhanced ranking by applying a hybridautomatic repeat request process that maintains the ranking constructedfor the initial transmission in the enhanced ranking for each of the oneor more users for which a re-transmission is to be performed, andpermits modification of the ranking constructed in the initialtransmission for each of the one or more users lacking theretransmission. The method additionally includes deploying, by theprocessor, the enhanced ranking into a schedule for the one or moreresource blocks being utilized by each of the one or more users. Themethod further includes optimizing, by the processor, bandwidth usage inthe one or more resource blocks by utilizing the schedule.

According to yet another aspect of the present principles, a system isprovided for enhanced long-term evolution scheduling. The systemincludes a processor and a memory. The processor and the memory areconfigured to construct a ranking for one or more users scheduled on oneor more resource blocks by assigning a precoder to each of the one ormore users. The processor and the memory are further configured togenerate an enhanced ranking that reduces a number of precodercomputations on the one or more resource blocks, by only initiating aprecoder computation when a precoder computation criterion is met. Theprocessor and the memory are additionally configured to deploy theenhanced ranking into a schedule for the one or more resource blocksbeing utilized by each of the one or more users. The processor and thememory are also configured to optimize bandwidth usage in the one ormore resource blocks by utilizing the schedule.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 shows a block diagram of an exemplary processing system to whichthe present invention may be applied, in accordance with an embodimentof the present invention;

FIG. 2 shows a block diagram of an exemplary environment to which thepresent invention can be applied, in accordance with an embodiment ofthe present invention;

FIG. 3 is a block diagram illustrating a method for enhanced schedulingon an LTE network, in accordance with an embodiment of the presentinvention;

FIG. 4 is a block diagram illustrating another method for enhancedscheduling on an LTE network, in accordance with an embodiment of thepresent invention; and

FIG. 5 is a block diagram illustrating yet another method for enhancedscheduling on an LTE network, in accordance with an embodiment of thepresent invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The invention improves the DL MU-MIMO scheduler for LTE advanced massiveMIMO systems. Different embodiments can be used singly or in combinationtogether. Several useful embodiments include: (i) processing the outputto enforce finite modulation and coding scheme (MCS) and finite bufferconstraints; (ii) incorporating hybrid automatic repeat request (HARQ)and (iii) including complexity reduction features that also exploit thedecorrelating property of massive MIMO systems.

An embodiment considers the DL wideband MU-MIMO scheduling problem ineach cell of an LTE-A network, where a scheduling decision must bedetermined every sub-frame. This involves selecting users on eachnarrowband resource block (RB), where a selected user can be assignedmore than one stream (a.k.a. a transmit rank greater than 1). However,there is a coupling constraint in that a user that is selected onmultiple RBs must be assigned the same transmit rank on all those RBs.It is noted that the flexibility of allowing multiple streams per useris important especially in practical massive MIMO scenarios where eachactive user has multiple receive antennas and the number of such usersis not large compared to the number of transmit antennas at the BS.Moreover, as the number of antennas increase the channel vectorscorresponding to different users become increasingly decorrelated. TheDL narrowband user selection has been analyzed mainly for the case wheneach user has one receive antenna and hence can be assigned one stream.Unfortunately, this is intractable and has been shown to be even hard toapproximate. Consequently, several heuristics are proposed. The DLwideband MU-MIMO scheduling with the aforementioned per-userrank-constraint has been only considered for specific values of theinput parameters (such as the maximum number of co-scheduled users,maximum rank per user etc.).

One embodiment significantly enhances the basic rank-balancingalgorithm. It shows that the resulting algorithm achieves a meaningfulapproximation guarantee for the general wideband LTE-A DL MU-MIMOscheduling problem, that scales as

$\frac{1}{l^{MU}\log \; },$

where l is the maximum number of streams that can be assigned to anyuser and l^(MU) denotes the maximum number of users that can bescheduled on any RB.

This embodiment conducts a thorough system level evaluation of thealgorithm by emulating an LTE-A massive MIMO network. The emulatednetwork is comprised of multiple cells operating in a standalone fashionand each cell is served by a BS equipped with a large antenna array. Itis noted that using stochastic geometry tools have demonstrated therelative advantages of standalone operation over one that entailscooperation.

This embodiment demonstrates the gains that can be achieved over abaseline system in which each cell is served by a 2 transmit antenna BS.These gains are obtained for several different antenna array sizes andinter-site-distances (ISDs).

Another embodiment considers a wideband DL MU-MIMO cell with M_(t)transmit antennas at the base station (BS) and M_(r) receive antennas ateach user k, where M_(t)≧M_(r). It is assumed K active users in the cellof interest and a total of N RBs (in each scheduling interval) availablefor data transmission. The signal received by the kth user on the nth RBis modeled as

y _(k,n) =H _(k,n) x _(n)+η_(k,n) ,k=1, . . . ,K,n=1, . . . ,N,  (1)

where H_(k,n)∈C^(M) ^(r) ^(×M) ^(t) is the channel matrix andη_(k,n)˜C^(M) ^(r) ^(×M) ^(t) is the additive noise plusinter-cell-interference (ICI). Notice that without loss of generality itis assumed a noise-plus-ICI whitening operation at the user so that thechannel matrix given in (1) is obtained post-whitening. The signalvector x_(n) transmitted by the BS on the nth RB can be expanded asx_(n)=Σ_(k∈U) _((n)) V_(k,n)s_(k,n), where U^((n)) is the set of usersco-scheduled (grouped) on the nth RB. V_(k,n), k∈U^((n)) is theM_(t)×r_(k) ^((n)) transmit precoding matrix used to transmit to the kthuser on the nth RB and has r_(k) ^((n)) unit-norm columns. Henceforth,r_(k) ^((n)) is referred to as the rank assigned to user k on the nthRB. s_(k,n) is the r_(k) ^((n))×1 symbol vector intended for the kthuser on the nth RB. Furthermore, let S_(n)=Σ_(k∈U) _((n)) r_(k) ^((n))be the total number of co-scheduled streams on RB n. The total power forall streams in any RB is ρ. Both equal power allocation over allco-scheduled streams in each RB, as well equal power over allco-scheduled users are considered. In the former case the power for eachstream of user k∈U^((n)) on the nth RB is given by

$\rho_{k,n}^{\prime} = {\frac{\rho}{s_{n}}.}$

On the other hand, under equal power per-user, the power for each streamof user k∈U^((n)) on the nth RB is given by

$\rho_{k,n}^{\prime} = {\frac{\rho}{{U^{(n)}}r_{k}^{(n)}}.}$

The transmit precoders are constructed using the available channel stateinformation (CSI) (from which the channel estimates Ĥ_(k,n), ∀k, n areobtained at the BS). It is assumed that the zero forcing (ZF) method isemployed for constructing transmit precoders but note that the resultsapply to other precoding methods such as block diagonalization (BD). Itis noted that ZF precoding is usually considered in a scenario whereusers have a single receive antenna each so that a single stream can beassigned to each scheduled user. Next, the convention is adopted fordesigning ZF precoders is described. Consider any RB n and any givenuser set U^((n)) along with a feasible rank vector r^((n))=[r₁ ^((n)), .. . , r_(k) ^((n))], such that r_(k) ^((n))=0 for any user k∉U^((n))while r_(k) ^((n))≧1 for any user k∈U^((n)). It is assumed that eachuser k∈U^((n)) that is assigned rank r_(k) ^((n)) on RB n will receivedata only post-filtering using a set of assigned r_(k) ^((n)) leftsingular vectors of the channel estimate Ĥ_(k,n). To identify aparticular set of r_(k) ^((n)) vectors (also referred to here as modes)out of the available M_(r) ones for each user, the binary valued M_(r)×Kmatrix M^((n)) is used. In particular, M_(i,k) ^((n))=1 (M_(i,k)^((n))=0) denotes that the i^(th) mode is (not) selected for user k onRB n. For any given such matrix M^((n)), it obtains the r_(k)^((n))×M_(t) matrix {tilde over (H)}_(k,n)=Û_(k,n) ^(†)Ĥ_(k,n),∀k∈U^((n)), where Û_(k,n) is the M_(r)×r_(k) ^((n)) filter matrix whosecolumns are the vectors identified by M^((n)) for user k. Theconstruction of the transmit precoder proceeds by using the matrices{{tilde over (H)}_(k,n)}_(k∈U) _((n)) as follows. Let {tilde over(H)}_(n)=([{tilde over (H)}_(k,n) ^(†)]_(k∈U) _((n)) )^(†) denote the(Σ_(k∈U) _((n)) r_(k) ^((n)))×M_(t) composite matrix. It obtains thematrix V_(n)={tilde over (H)}_(n) ^(†)({tilde over (H)}_(n){tilde over(H)}_(n) ^(†))⁻¹D_(n) where D_(n) is a diagonal matrix which normalizesall columns of {tilde over (H)}_(n) ^(†)({tilde over (H)}_(n){tilde over(H)}_(n) ^(†))⁻¹ to have unit norm. Then V_(k,n) is obtained as thesub-matrix of V_(n) formed by the r_(k) ^((n)) columns corresponding touser k. Let ξ(M^((n)),n) denote the resulting weighted sum rate on thenth RB, where

${\xi \left( {M^{(n)},n} \right)} = {\sum\limits_{k = 1}^{K}{\underset{\underset{= {\xi {({M^{(n)},\; n})}}}{}}{\sum\limits_{i = 1}^{M_{r}}{\xi_{i,k}\left( {M^{(n)},n} \right)}} \cdot {\xi \left( {M^{(n)},n} \right)}}}$

denotes the weighted rate obtained on the i^(th) mode and nth RB foruser k and is given by

ξ_(i,k)(M ^((n)) ,n)=w _(k) log(1+ρ_(k,n)′γ_(i,k,n)),i:M _(i,k)^((n))=1  (2)

With ξ_(i,k)(M^((n)),n)=0,i:M_(i,k) ^((n))=0. Here, w_(k) denotes theweight of user k and γ_(i,k,n) is the effective gain. This gain equalsthe squared norm of the component of the column in {tilde over (H)}_(n)^(†) corresponding to mode i of user k, in the orthogonal complement ofthe span of all other columns in {tilde over (H)}_(n) ^(†).

Now consider any set of co-scheduled user U^((n)) along with a feasiblerank vector r^((n)). The optimal weighted sum rate (under our ZFprecoding convention) for this choice is given by

${\xi \left( {U^{(n)},r^{(n)},n} \right)} = {\max\limits_{{M \in {{({0,1})}^{M_{r} \times K\sum\limits_{i = l}^{M_{r}}}M_{i,k}{\infty r}_{k}^{(n)}}},{\forall i}}{\xi \left( {M,n} \right)}}$

Next, a first observation is stated. This observation has been formallyproved for the case of single-stream per-user ZF precoding with fullpower optimization.

Lemma 1 Let e_(j), 1≦j≦K denote a basis vector of length K with itsentry equal to one in its j^(th) position and zero elsewhere. Then,

$\begin{matrix}{{\xi \left( {U^{(n)},r^{(n)},n} \right)} \leq {\sum\limits_{{keU}^{(n)}}{{\xi \left( {\left\{ k \right\},{r_{k}^{(n)}e_{k}},n} \right)}.}}} & (3)\end{matrix}$

Yet another embodiment considers the MU-MIMO scheduling problem for awideband system with N RBs to find the joint optimal user grouping, modeand RB allocations which maximize the weighted sum rate. The first mainpractical constraint that is imposed here is the per-user rankconstraint, i.e., the rank assigned to a user should be identical on allits allocated RBs. Then, dimensioning constraints are incorporated whichdictate that on any RB assigned to more than one user, no more thanl^(MU) users can be co-scheduled, no more than l^(MU) layers can beassigned to any scheduled user and no more than L^(MU) layers can beassigned across all scheduled users. Clearly, without loss of generalitywe can assume l^(MU)≦L^(MU). On the other hand, on any RB assigned tojust one user, no more than l layers can be assigned to that user and wemake a natural assumption that 1≦l^(MU)≦l≦M_(r). Denote N as the set ofRBs that are available for scheduling, where N={1, . . . , N}. TheMU-MIMO scheduling problem is posed here as

$\begin{matrix}{{\max\limits_{\{{{U^{n)} \in U},{{r^{(n)}n} \in N}}\}}{\sum\limits_{n \in N}{\xi \left( {U^{(n)},r^{(n)},n} \right)}}},} & \; \\\left. {{s.t.{U^{(n)}}} \geq 2}\Rightarrow\left\{ {{{\begin{matrix}{{\sum\limits_{k \in U^{(n)}}r_{k}^{(n)}} \leq L^{MU}} \\{{r^{(n)}}_{\infty} \leq ^{MU}} \\{{U^{(n)}} \leq l^{MU}}\end{matrix}{U^{(n)}}} = {\left. 1\Rightarrow{{r^{(n)}}_{\infty} \leq {r_{k}^{(s)}}} \right. = r_{k}^{(m)}}},{{{if}\mspace{14mu} k} \in {U^{(n)}\bigcap U^{(m)}}},{{\forall{n \neq {m.r_{k}^{(n)}}}} = 0},{{{{\forall{k \notin U^{(n)}}}\&}\mspace{11mu} r_{k}^{(n)}} \geq 1},{\forall{k \in {U^{(n)}{\forall{n.}}}}}} \right. \right. & (4)\end{matrix}$

In LTE-A (LTE Rel. 10), l^(MU)=L^(MU)=4 and l^(MU)=2 but these can besignificantly more relaxed for massive MIMO systems. The problem in (4)can be ascertained to be NP-hard in general since it subsumes simplerscheduling problems that are already known to be hard.

Consider the following scheduling problem on any RB n.

$\begin{matrix}{\max\limits_{{{A \in U}{A \leq l^{MU}}},4}\left\{ {\xi \left( {A,d,n} \right)} \right\}} & \; \\{{{{{{\sum\limits_{k \in A}d_{k}} \leq L^{MU}}\&}\mspace{11mu} 1\left\{ {k \in A} \right\}} \leq d_{k} \leq {^{MU}1\left\{ {k \in A} \right\}}},{\forall{k \in U}},{{A} \geq {2\mspace{11mu} 1\left\{ {k \in A} \right\}} \leq d_{k} \leq {\; 1\left\{ {k \in A} \right\}}},{\forall{k \in U}},{{A} = 1},} & (5)\end{matrix}$

Where 1 {.} denotes an indicator function that is one if the inputargument is true and is zero otherwise. The special case where each userhas one antenna and hence can be assigned at-most one layer has beenrecently considered and analyzed. The results are first extended todifferent choices of transmit power allocation and where each scheduleduser can be assigned any arbitrarily fixed rank. Letting the rank fixedfor user k (when scheduled) to be r_(k)*:1≦r_(k)*≦l^(MU) we consider asimplified version on any RB n,

$\begin{matrix}\begin{matrix}{\max\limits_{A \in U}\left\{ \; {\xi \mspace{11mu} \left( {A,n} \right)} \right\}} \\{{{A} \leq l^{MU}},{{\sum\limits_{k\; \in A}r_{k}^{*}} \leq L^{MU}},}\end{matrix} & (6)\end{matrix}$

it further adopts the convention that ξ(A,n)=0 whenever the ZF transmitprecoder construction is not possible. Notice now that the objectivefunction can be viewed as a normalized non-negative set function definedon all subsets on U, which outputs a real (non-negative) value for eachpossible input set. This function would also be a submodular setfunction provided

ξ(A∪{u},n)−ξ(A,n)≧ξ(B∪{u},n)−ξ(B,n),

∀A⊂B&u∈U\B.  (7)

The proof is based on a counter-example that can be constructed.

The implication that simple greedy methods need not guarantee aconstant-factor approximation even for the simpler problems.Nevertheless, since the exhaustive search is in general impractical,consider the Greedy Search to solve the problem. This greedy search is anatural adaptation that a simple performance bound can be asserted. Ateach stage of this greedy search, the gain is evaluated in weighted sumrate obtained by adding one mode to an existing user or to a new user(subject to feasibility constraints), and determine the best possiblechoice resulting in the largest gain in weighted sum rate. This choiceis accepted if the gain is positive else the process terminates. For thefinal selection, the weighted sum rate of the output obtained upontermination is compared against the best single-user weighted rate andthe selection corresponding to larger rate is chosen. Note that bestsingle-user weighted rate, which is the optimal solution on the RB ofinterest under the restriction that it be assigned to only one user, canbe readily determined (as detailed in the appendix). Then, since aselection at-least as good as the best single user choice is chosen andno more than l^(MU) users can be co-scheduled, l≧l^(MU) and invoke theproperty stated in (3) to deduce the following result. The greedy searchyields a selection yielding a weighted sum rate that is at-least aslarge as

$\frac{1}{l^{MU}}$

times the optimal objective value.

Still another embodiment presents and analyzes a rank balancing basedscheduling algorithm that is applicable to any arbitrary inputdimensioning parameters L^(MU), l^(MU), l^(MU), l^(SU). It is noted thata particular case of this algorithm that applies to l^(MU)=2,l^(MU)=L^(MU)=4. More importantly, in a post-processing stageenhancements are incorporated that are necessary for practicalimplementation such as speed-ups, finite constraints on buffers andfinite MCSs and enhanced HARQ support. The detailed procedure isprovided. The key steps of the proposed rank balancing method are thefollowing.

-   -   Step(1) Greedy search without the per-user rank constraint: For        each RB n, the weighted sum rate is optimized over user, mode        selections, and determine the optimized user and mode choices        ^((n)),        ^((n)). Let r^((n)) denote the associated rank selection.    -   Step(2) Fix the per-user rank through rank balancing: For each        user k, we obtain q_(k,m) which is its sum weighted rate over        all RBs n∈N with        _(k) ^((n))=m, for each rank m. q_(k,m) is added to certain        weighted rate estimates from other RBs on which user k is        assigned a rank larger that m in Step (1) to obtain {hacek over        (q)}_(k,m). Then, rank m* is found which results in the highest        estimated weighted sum rate for user k and set r_(k)*=m*.    -   Step(3) Based on the determined user rank vector r*, user is        refined, mode selections on each RB, where rank of each user is        restricted in the considered user set to be its corresponding        rank in r*. Note that on each RB n, the basic refinement begins        by setting Ũ^((n))=φ, {tilde over (M)}^((n))=0. Then, for each        user k∈        ^((n)):{hacek over (r)}_(k) ^((n))≧r_(k)*, k is added to Ũ^((n))        and select for that user in {tilde over (M)}^((n)) the r_(k)*        modes yielding the top r_(k)* largest elements from {ξ_(i,k)(        ^((n)),n)}_(i=1) ^(M) ^(r) . For any other user k∈        ^((n)):{hacek over (r)}_(k) ^((n))≧r_(k)*, no mode is selected        and no user is added to Ũ^((n)).

Note that Step (3) should not be applied to any RB n:{hacek over(r)}_(k) ^((n))=r_(k)*, ∀k∈

^((n)). Also, further refinement can be optionally done to improveξ({tilde over (M)}^((n)), n) without changing the non-zero determinedranks in r*.

Initializations: N={1, . . . , N}, U={1, . . . , K}, and r*=0. each n∈NOptimize the weighted sum rate ξ(M,n) over user, mode allocations A,Msuch that ∥M∥₁≦L^(MU) and 1{k∈A}≦Σ_(i=1) ^(M) ^(r)M_(i,k)≦l^(MU)1{k∈A}∀k where 2≦|A|≦l^(MU), as well as over eachsingleton set A={k} with ∥M∥₁Σ_(i=1) ^(M) ^(r) M_(i,k)≦l. Denote theoptimized allocations by {

^((n)),

^((n))} and let {hacek over (r)}^((n)) be the corresponding optimizedranks. For each k∈U_(n)

^((n)) and each m Obtain q_(k,m)=Σ_(n:{hacek over (r)}) _(k) ^((n))_(=m)ξ_(k)(

^((n)),n). Set {tilde over (q)}_(k,m)=q_(k,m). For each n:

_(k) ^((n))>m, update {tilde over (q)}_(k,m)={tilde over(q)}_(k,m)+Δ_(k,m)(

^((n)),n), where Δ_(k,m)(

^((n)),n) is the sum of the m largest elements from {ξ_(l,k)(

^((n)),n)}_(i=1) ^(M) ^(r) . For each user k∈U_(n)

^((n)), find r_(k)*=argmax_(m){tilde over (q)}_(k,m). Refine the userand mode selections on each RB n∈N, to obtain the optimized output.

The following theorem proves that this embodiment for MU-MIMO scheduling(rank balancing method) has a worst-case performance guarantee. We let

${{H(j)} = {1 + \frac{1}{2}}},{\ldots + \frac{1}{j}},{\forall{j \geq 1.}}$

Theorem 1 This embodiment achieves

$\frac{1}{I^{{MU}_{H{()}}}}$

approximation to the MU-MIMO scheduling problem (4).Proof: First, the greedy search yields a selection yielding a weightedsum rate that is at-least as large as

$\begin{matrix}\frac{1}{l^{MU}} & \;\end{matrix}$

times the optimal objective value to deduce that the weighted sum ratedetermined on each RB in Step (1) is at-least

$\frac{1}{l^{MU}}$

times the optimal one for that RB. Thus, the weighted sum rate acrossall RBs is at-least

$\frac{1}{l^{MU}}$

times the sum of the per-RB optimal weighted sum rates across all RBs.Since the latter sum ignores the per-user rank constraint it is clearlyan upper bound to the optimal solution of the MU-MIMO scheduling problem(4). Next, the worst-case loss due to the rank balancing step ischaracterized and shows that the final solution from this embodiment isguaranteed to achieve

$\frac{1}{H()}$

times the weighted sum rate across all RBs obtained after Step (1).Thus, the final output yields a weighted sum rate that is at-least

$\frac{1}{l^{MU}{H()}}$

of the optimal solution of (4), thereby proving the theorem. Then notethat the weighted rate for user k after Step (1) is Σ_(m=1) ^(l)q_(k,m), so that the overall weighted sum rate is Σ_(k∈U) Σ_(m=1) ^(l)q_(k,m). Further, by construction, we have that

${\overset{\sim}{q}}_{k,r_{k}^{*}} \geq {\max_{m = 1}^{}{\left\{ {q_{k,m} + {\sum_{m^{\prime} > m}{\frac{m}{m^{\prime}}q_{k,m^{\prime}}}}} \right\}.}}$

Therefore, that ratio

$\frac{{\overset{\sim}{q}}_{k,r_{k}^{*}}}{\sum_{m = 1}^{}q_{k,m}}$

is at-least

$\begin{matrix}{\min\limits_{x \in {1R_{m}^{}}}{\left\{ \frac{\underset{m = 1}{\max\limits^{}}\left\{ {x_{m} + {\sum\limits_{m^{\prime} > m}{\frac{m}{m^{\prime}}x_{m^{\prime}}}}} \right\}}{\sum\limits_{m = 1}^{}x_{m}} \right\}.}} & (8)\end{matrix}$

The solution to the problem in (8) can be determined using a generalresult, as

$\begin{matrix}\frac{1}{1^{T}G^{- 1}1} & (9)\end{matrix}$

where G for us is an l×l lower triangular matrix which has entries

${G_{i,j} = \frac{j}{i}},{\forall{i \geq {j.}}}$

Thus G⁻¹ is a bidiagonal lower triangular matrix with

${G_{i,i} = {{{{1{\forall i}}\&}G_{i,{i - 1}}} = \frac{- \left( {i - 1} \right)}{i}}},{\forall{i \geq 2.}}$

Thus, we have that

$\begin{matrix}{\frac{1}{1^{T}G^{- 1}1} = {\frac{1}{H()}.}} & (10)\end{matrix}$

Notice then, that the basic refinement step obtains Ũ^((n)), {tilde over(M)}^((n)). It can be seen that since on each RB and for each userscheduled on that RB after Step (1), we retain only a subset of theassigned modes, we will have Σ_(n∈N)ξ_(k)({tilde over(M)}^((n)),n)≧q_(k,r) _(k) _(*), ∀k. Since further refinement will onlyimprove the solution at hand, we have the desired result.

In order to use the rank balancing proposed above for LTE scheduling weneed to incorporate finite MCS, finite buffers and HARQ. The relatedenhancements are described that form the post-processing stage. Thisstage begins after the output from rank balancing has been obtained. Theenhancements can be done in embodiments individually or in embodimentstogether as combinations. The enhancements when employed in an LTEsystem increase the efficiency of the system by better managing the userrequests on the system for an optimized use of the available bandwidthby reducing the need for re-transmission of data to the user,efficiently handling re-transmission of the user, aligning a user's datausage across all RBs, or aligning a user's ranking across all RBs.

Finite MCS and Finite Buffers:

The MU-MIMO scheduling output is used and users are processed in asequential manner. In one embodiment, the processing order is obtainedby sorting the weighted sum rates of the users across all RBs in thedescending order. For each user under consideration, the rank determinedby the algorithm is used and all RBs on which it is scheduled arecollected. Note that the assigned rank determines the codeword to layermapping. The collected RBs are sorted in the descending order of theweighted rates achieved on those RBs by the user of interest. Then itdetermines and assigns a subset of the top RBs from the sorted set. Thissubset is determined by maximizing the rate achieved with the availablefinite MCS and under the finite buffer constraint. The top RBs areconsidered from a sorted subset, the complexity of determining thesubset scales only linearly in the number of RBs N. The remaining RBsnot in the subset (if any) are vacated by the user. For each such RB, incase any of the other co-scheduled users have not yet been processed,the further refinement step can be repeated, albeit using the pool ofonly un-processed users. Otherwise, if at-least one processed user hasbeen assigned that RB, the signal-to-interference-plus-noise ratios(SINRs) of other un-processed co-scheduled users are re-computed sincethey would have improved.

Speed-Ups:

Additional restrictions are imposed in order to reduce complexity oradditional conditions are checked when optimizing the narrowband problemon each RB n. These include:

-   -   Imposing a rank restriction that for any user set A⊂U:|A|≧2, a        permissible rank vector must satisfy ∥d∥_(∞)≦1, but ∥d∥_(∞)≦l        when |A|=1. In other words, SU assignments are searched for with        ranks up to l but restrict MU assignments to co-scheduling users        with ranks identical to 1. Such a restriction is also beneficial        in terms of mitigating the impact of imperfect CSI. Another        example is where the rank of some user k is fixed to a given        input. Such a restriction is useful to handle re-transmission        users, as described below.    -   Enforcing that the modes for any user can only be assigned in a        fixed per-determined order (for instance the one corresponding        to the descending order of respective singular values). Further,        rank balancing procedure can be done using only {tilde over        (q)}_(k,m)=q_(k,m), ∀k, m without the update in step-8 and the        basic refinement can be simplified accordingly. It can be shown        that the resulting approximation factor degrades to

$\frac{1}{l^{MU}},$

which is acceptable for small l.

-   -   Further complexity reduction can be obtained by reducing the        number of precoder computations (without any performance        degradation) as follows. Check whether the inclusion of a new        user or layer meets a necessary condition for improving the        weighted sum rate and initiate the precoder computation only        upon passing the condition check. The following three        progressively tighter necessary conditions are evaluated:        -   (A) Imposing a basic condition which computes an upper bound            on the weighted sum rate assuming that any candidate            user: (i) will see no interference from already selected            ones (so we can use its single user reported CSI) and (ii)            in turn will cause no interference to those already selected            so that we re-use the SINRs that have been computed for such            users. Accounting for power splitting between the candidate            user and those already selected when computing the upper            bound.        -   (B) The second tighter necessary condition exploits the fact            that the effective channel gain seen by any candidate user            decreases as the interfering set of already selected users            grows. The most-recently computed SINRs can be used for any            candidate. These would have been computed in a previous            iteration when that candidate user passed the condition            check but was not the best user in that iteration and hence            was not selected.        -   (C) The third condition which is further tighter, exploits            property stated in (B) for the already selected users as            well. Instead of assuming that the already selected users            see no interference from the candidate user, for each            already selected user we use the minimum among the SINR            computed in the previous iteration upon adding that            candidate user and the SINR computed in the previous            iteration upon adding the user selected as best user in that            iteration. The cost of computing the enhanced upper bound            used in this tighter condition is almost the same as that in            the basic one since we are re-using the terms that are            anyway computed.

HARQ:

The key feature it uses is to schedule re-transmission users by firstincluding them in a common pool along with first transmission users.Then, for this common pool the scheduling output is obtained, with therestriction that the assigned rank of each re-transmission user must bethe same as the one used for its first transmission. Next, in thepost-processing stage while processing a re-transmission user it furtherlimits its top RBs subset size to not exceed the number of RBs assignedto it in its first transmission.

FIG. 1 shows a block diagram of an exemplary processing system 100 towhich the invention principles may be applied, in accordance with anembodiment of the present invention. The processing system 100 includesat least one processor (CPU) 104 operatively coupled to other componentsvia a system bus 102. A cache 106, a Read-Only Memory (ROM) 108, aRandom-Access Memory (RAM) 110, an input/output (I/O) adapter 120, asound adapter 130, a network adapter 140, a user interface adapter 150,and a display adapter 160, are operatively coupled to the system bus102.

A first storage device 122 and a second storage device 124 areoperatively coupled to system bus 102 by the I/O adapter 120. Thestorage devices 122 and 124 can be any of a disk storage device (e.g., amagnetic or optical disk storage device), a solid state magnetic device,and so forth. The storage devices 122 and 124 can be the same type ofstorage device or different types of storage devices.

A speaker 132 is operatively coupled to system bus 102 by the soundadapter 130. The speaker 132 can be used to provide an audible alarm orsome other indication relating to resilient battery charging inaccordance with the present invention. A transceiver 142 is operativelycoupled to system bus 102 by network adapter 140. A display device 162is operatively coupled to system bus 102 by display adapter 160.

A first user input device 152, a second user input device 154, and athird user input device 156 are operatively coupled to system bus 102 byuser interface adapter 150. The user input devices 152, 154, and 156 canbe any of a keyboard, a mouse, a keypad, an image capture device, amotion sensing device, a microphone, a device incorporating thefunctionality of at least two of the preceding devices, and so forth. Ofcourse, other types of input devices can also be used, while maintainingthe spirit of the present invention. The user input devices 152, 154,and 156 can be the same type of user input device or different types ofuser input devices. The user input devices 152, 154, and 156 are used toinput and output information to and from system 100.

Of course, the processing system 100 may also include other elements(not shown), as readily contemplated by one of skill in the art, as wellas omit certain elements. For example, various other input devicesand/or output devices can be included in processing system 100,depending upon the particular implementation of the same, as readilyunderstood by one of ordinary skill in the art. For example, varioustypes of wireless and/or wired input and/or output devices can be used.Moreover, additional processors, controllers, memories, and so forth, invarious configurations can also be utilized as readily appreciated byone of ordinary skill in the art. These and other variations of theprocessing system 100 are readily contemplated by one of ordinary skillin the art given the teachings of the present invention provided herein.

Moreover, it is to be appreciated that environment 200 described belowwith respect to FIG. 2 is an environment for implementing respectiveembodiments of the present invention. Part or all of processing system100 may be implemented in one or more of the elements of environment200.

Further, it is to be appreciated that processing system 100 may performat least part of the method described herein including, for example, atleast part of method 300 of FIG. 3 and/or at least part of method 400 ofFIG. 4 and/or at least part of method 500 of FIG. 5.

FIG. 2 shows an exemplary environment 200 to which the present inventioncan be applied, in accordance with an embodiment of the presentinvention. The environment 200 is representative of a cellular networkto which the present invention can be applied. The elements shownrelative to FIG. 2 are set forth for the sake of illustration. However,it is to be appreciated that the present invention can be applied toother network configurations as readily contemplated by one of ordinaryskill in the art given the teachings of the present invention providedherein, while maintaining the spirit of the present invention.

The environment 200 may include a user equipment (UE) 210. In oneembodiment, the UE 210 may be a cellphone. In another embodiment, the UE210 may be a tablet, laptop, or other device that can use a wirelessconnection. The UE 210 may send data and information over acommunication link 220. The communication link 220 may include acellular based or a WIFI based link. The UE 210 is communicating with acellular tower 230. The information or data sent from the UE 210 to thecellular tower 230 is transmitted by another communication link 240 toan LTE node 250.

Referring to FIG. 3, a block diagram illustrating an enhanced schedulingmethod 300 for an LTE network, in accordance with an embodiment of thepresent invention. An example of embodiment (i) from above: processingthe output to enforce finite modulation and coding scheme (MCS) andfinite buffer constraints. In block 310, construct a ranking for one ormore users scheduled on one or more resource blocks. The ranking isassigning a transmit rank (or the number or streams or layers) for thatuser. In block 320, generate, using a finite modulation and codingscheme, a layer mapping utilizing the ranking of each of the one or moreusers for the one or more resource blocks. In block 330, determine,using a finite constraint on a buffer for each of the one or more users,an enhanced ranking for the one or more resource blocks utilizing thelayer mapping. In block 340, deploy the enhanced ranking into a schedulefor the one or more resource blocks being utilized by each of the one ormore users. In block 350, optimize bandwidth usage in the one or moreresource blocks by utilizing the schedule.

Referring to FIG. 4, a block diagram illustrating an enhanced schedulingmethod 400 for an LTE network, in accordance with an embodiment of thepresent invention. An example of embodiment (ii) from above:incorporating hybrid automatic repeat request (HARQ). In block 410,construct a ranking for one or more users scheduled on one or moreresource blocks. In block 420, generating an enhanced ranking byapplying a hybrid automatic repeat request process that maintains theranking constructed for the initial transmission in the enhanced rankingfor each of the one or more users for which a re-transmission is to beperformed, and permits modification of the ranking constructed in theinitial transmission for each of the one or more users lacking theretransmission. In block 430, deploy the enhanced ranking into aschedule for the one or more resource blocks being utilized by each ofthe one or more users. In block 440, optimize bandwidth usage in the oneor more resource blocks by utilizing the schedule.

Referring to FIG. 5, a block diagram illustrating an enhanced schedulingmethod 500 for an LTE network, in accordance with an embodiment of thepresent invention. An example of embodiment (iii) from above: includingcomplexity reduction features that also exploit the decorrelatingproperty of massive MIMO systems. In block 510, construct a ranking forone or more users scheduled on one or more resource blocks by assigninga precoder to each of the one or more users. In block 520, generate anenhanced ranking that reduces a number of precoder computations on theone or more resource blocks, by only initiating a precoder computationwhen a precoder computation criterion is met. In block 530, deploy theenhanced ranking into a schedule for the one or more resource blocksbeing utilized by each of the one or more users. In block 540, optimizebandwidth usage in the one or more resource blocks by utilizing theschedule.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid statememory, magnetic tape, a removable computer diskette, a random accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

Each computer program may be tangibly stored in a machine-readablestorage media or device (e.g., program memory or magnetic disk) readableby a general or special purpose programmable computer, for configuringand controlling operation of a computer when the storage media or deviceis read by the computer to perform the procedures described herein. Theinventive system may also be considered to be embodied in acomputer-readable storage medium, configured with a computer program,where the storage medium so configured causes a computer to operate in aspecific and predefined manner to perform the functions describedherein.

A data processing system suitable for storing and/or executing programcode may include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code to reduce the number of times code is retrieved frombulk storage during execution. Input/output or I/O devices (includingbut not limited to keyboards, displays, pointing devices, etc.) may becoupled to the system either directly or through intervening I/Ocontrollers.

Network adapters may also be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modem and Ethernet cards are just a few of thecurrently available types of network adapters.

Reference in the specification to “one embodiment” or “an embodiment” ofthe present invention, as well as other variations thereof, means that aparticular feature, structure, characteristic, and so forth described inconnection with the embodiment is included in at least one embodiment ofthe present invention. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment”, as well any other variations,appearing in various places throughout the specification are notnecessarily all referring to the same embodiment.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention. Having thus described aspects of the invention,with the details and particularity required by the patent laws, what isclaimed and desired protected by Letters Patent is set forth in theappended claims.

What is claimed is:
 1. A computer-implemented method for enhancedscheduling on a long-term evolution network, the method comprising:constructing, by a processor, a ranking for one or more users scheduledon one or more resource blocks; generating, by the processor using afinite modulation and coding scheme, a layer mapping utilizing theranking of each of the one or more users for the one or more resourceblocks; determining, by the processor using a finite constraint on abuffer for each of the one or more users, an enhanced ranking for theone or more resource blocks utilizing the layer mapping; deploying, bythe processor, the enhanced ranking into a schedule for the one or moreresource blocks being utilized by each of the one or more users; andoptimizing, by the processor, bandwidth usage in the one or moreresource blocks by utilizing the schedule.
 2. The computer-implementedmethod of claim 1, wherein said constructing step includes ranking eachof the one or more users on each of the one or more resource blocks andbalancing the ranking for each of the one or more users across the oneor more resource blocks to provide a balanced ranking.
 3. Thecomputer-implemented method of claim 1, wherein said generating stepprocesses each of the one or more users in a descending sequential orderaccording to the ranking of each of the one or more users, by sortingweighted sum rates of each of the one or more users across all of theone or more resource blocks.
 4. The computer-implemented method of claim3, wherein said sorting step sorts the one or more resource blocks intoa subset, with any of the one or more resource blocks that are absentfrom the subset being removed from consideration for use by the one ormore users.
 5. The computer-implemented method of claim 1, wherein saiddetermining step includes utilizing a signal-to-interference-plus-noiseratio for each of the one or more users in the layer mapping.
 6. Thecomputer-implemented method of claim 5, wherein said utilizing stepincludes re-computing the signal-to-interference-plus-noise ratio forthe one or more users absent from the layer mapping.
 7. Thecomputer-implemented method of claim 1, wherein the layer mappingincludes all of the one or more resources blocks that each of the one ormore users is scheduled to utilize.
 8. A non-transitory article ofmanufacture tangibly embodying a computer readable program which whenexecuted causes a computer to perform the steps of claim
 1. 9. Acomputer-implemented method for enhanced scheduling on a long-termevolution network, the method comprising: constructing, by a processor,a ranking for one or more users scheduled for an initial transmission onone or more resource blocks; generating, by a processor, an enhancedranking by applying a hybrid automatic repeat request process thatmaintains the ranking constructed for the initial transmission in theenhanced ranking for each of the one or more users for which are-transmission is to be performed, and permits modification of theranking constructed in the initial transmission for each of the one ormore users lacking the retransmission; deploying, by the processor, theenhanced ranking into a schedule for the one or more resource blocksbeing utilized by each of the one or more users; and optimizing, by theprocessor, bandwidth usage in the one or more resource blocks byutilizing the schedule.
 10. The computer-implemented method of claim 9,wherein said constructing step includes ranking each of the one or moreusers on each of the one or more resource blocks and balancing theranking for each of the one or more users across the one or moreresource blocks to provide a balanced ranking.
 11. Thecomputer-implemented method of claim 9, wherein the hybrid automaticrepeat request process places the one or more users requiringre-transmission and other users in a common pool before restricting theone or more users requiring re-transmission to have the same ranking.12. The computer-implemented method of claim 9, further includinglimiting a number of resource blocks used by the one or more usersrequiring re-transmission to remain equal to or less than an initialnumber of resource blocks the one or more users requiringre-transmission originally used to transmit.
 13. Thecomputer-implemented method of claim 9, wherein said optimizing stepincludes reducing the need for re-transmission of the one or more usersor aligning the ranking of the one or more users across the one or moreresource blocks.
 14. A non-transitory article of manufacture tangiblyembodying a computer readable program which when executed causes acomputer to perform the steps of claim
 9. 15. An enhanced long-termevolution scheduling system, the system comprising: a processor and amemory connected to the processor configured to: construct a ranking forone or more users scheduled on one or more resource blocks by assigninga precoder to each of the one or more users; generate an enhancedranking that reduces a number of precoder computations on the one ormore resource blocks, by only initiating a precoder computation when aprecoder computation criterion is met; deploy the enhanced ranking intoa schedule for the one or more resource blocks being utilized by each ofthe one or more users; and optimize bandwidth usage in the one or moreresource blocks by utilizing the schedule.
 16. The system of claim 15,wherein the ranking is constructed by ranking each of the one or moreusers on each of the one or more resource blocks and balancing theranking for each of the one or more users across the one or moreresource blocks to provide a balanced ranking.
 17. The system of claim15, wherein the enhanced ranking is generated by imposing a restrictedsearch process on the ranking of the one or more users.
 18. The systemof claim 17, wherein the restricted search process includes searchingall single-user assignments up to a maximum threshold and restrictingall multi-user assignments by co-scheduling the one or more users withpre-determined rankings.
 19. The system of claim 15, wherein theprecoder criterion includes improving a weighted sum rate for the one ormore resource blocks.
 20. The system of claim 15, wherein the precodercriterion is based on a presumption that a layer assigned to each of theone or more users causes no interference with a previously assignedlayer.